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I guess you want your transition matrix to be a square matrix and add a column corresponding to state zero as well. Not the answer you're looking for?Browse other questions tagged probability markov-chains or ask your own question.
Within the United States (Pittsburgh), when merging onto a lane, which turn signal do you use? What are some examples of when Mathematics 'accidentally' discovered something about the world? Photography Stack Exchange is a question and answer site for professional, enthusiast and amateur photographers. The image on the left is mine (combined data from two shots and heavily adjusted contrast and brightness and rotated), the one on the right is from NASA for reference.
Just noticed you are not asking about only reducing the brightness, but actually asking how to bring out any features of the Jupiter's surface.
The basic problem is the difference in brightness between Jupiter and the brightness of its moons. Well, you should try this: put the camera on a tripod, focus to infinity (use the same zoom settings you used for the Jupiter), and make test photos with different aperture settings under good lighting condition.
With long focal length astrophotography the need for speed almost always trumps the desire to use a medium aperture to maximize a lens' sharpness. Not the answer you're looking for?Browse other questions tagged astrophotography or ask your own question. What causes and how can I avoid this moiré pattern in a composite night sky photograph? Is it true that UFOs or extraterrestrial beings that are not seen by human eyes can be captured by photo?


For which n is there a permutation such that the sum of any two adjacent elements is a prime?
I got bored and took pictures of a bunch of stuff around the house using my son’s toy microscope. Last year, I worked my ass off on drawing a children’s book and now I am struggling to get it noticed.
My mom said she didn’t want to take down the last of the lights until the first snow. I think this means that A starts with 0 molecules, and something happened to make it have 1 molecule?
Ehrenfest for the movement of molecules in which M molecules are distributed among two urns. One advantage of cameras with smaller sensors is they gain telephoto "reach" with smaller, shorter focal length lenses.
With a narrow field of view, even very slight movements of the camera are highly magnified. You will have a series of pictures, and you will be able to determine what is the ideal aperture setting, what gives the sharpest results. If you choose a molecules uniformly at random, what is the probability that you chose one from urn A?
When you are in state $0$ and you choose a molecule at random, with probability $1$ is from urn $B$, and then you move it to urn $A$, obtaining state $1$. It was probably also done by a telescope at high altitude in clear air if not by a telescope in Earth orbit or even a deep space probe. Even when brightness is reduced in the second photo prior to RAW conversion until Jupiter is no longer at full saturation and the dimmer moons are about to fade out, there are no surface details of Jupiter that are recoverable.
Generally locations with cooler and drier air in the atmosphere above your viewing location will be more stable and provide better "seeing" than warmer, more humid air that is often turbulent as well.


If you roll over the images, it uses the setting on the right, if you do not, it uses the settings on the left.
And at the very least it is probably three combined images, each taken with a monochrome camera filtered for one of three different colors. Even with a lesser tripod brisk winds can cause subtle camera motion that affects your results.
It is difficult enough to get razor sharp focus using a large telephoto lens with a manual focus ring. Actuating the shutter button directly instead of using a timer or remote release also will likely add some camera movement. It is even more difficult to do so using a 'focus by wire system' that may not have intervals fine enough between steps. And any mechanical movement inside the camera associated with the shutter release can also introduce camera movement.
Because infinity focus changes with focal length and other environmental factors, most lenses allow the focusing elements to go past infinity. Although this is of primary concern with an SLR that has a mirror that moves, even stopping down the aperture or moving a mechanical shutter has the potential to introduce smaller amounts of shake. Many lenses with high speed AF motors allow an even greater buffer past infinity focus so the focus motor is less likely to bump against the end of travel when trying to focus at infinity.



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